Question

1. the number of fifth - graders buying lunch each day for nine days is shown. 90, 72, 48, 84, 77, 72, 50, 83 determine the value for each statistical measure. mean median mode range 42 75 72 72

Explanation:

Step1: Calculate the mean

The mean is the sum of all data - points divided by the number of data - points.
Sum = \(90 + 72+48 + 84+77+72+50+83\)
Sum \(=90+72\times2 + 48+84+77+50+83\)
Sum \(=90 + 144+48+84+77+50+83\)
Sum \(=234+48+84+77+50+83\)
Sum \(=282+84+77+50+83\)
Sum \(=366+77+50+83\)
Sum \(=443+50+83\)
Sum \(=493+83 = 576\)
Number of data - points \(n = 8\)
Mean\(=\frac{576}{8}=72\)

Step2: Calculate the median

First, order the data: \(48,50,72,72,77,83,84,90\)
Since \(n = 8\) (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered data - points.
\(\frac{n}{2}=4\) and \(\frac{n}{2}+1 = 5\)
Median\(=\frac{72 + 77}{2}=\frac{149}{2}=74.5\)

Step3: Calculate the mode

The mode is the data - point that appears most frequently.
The number \(72\) appears \(2\) times, and all other numbers appear only once. So the mode is \(72\).

Step4: Calculate the range

The range is the difference between the maximum and minimum values.
Maximum value \(=90\), minimum value \(=48\)
Range\(=90 - 48=42\)

Answer:

Mean: 72
Median: 74.5
Mode: 72
Range: 42